Consider the sequence 10.20, 11.40, 12.10, 13.40 where each term
represents the amount of money you earned as interest on your savings
account for each of four years.

The sum of the
terms, 10.2 + 11.4 + 12.1 + 13.4, represents the total interest
you earned in the four year period. Such a sequence
summation is called a series
and is designated by Snwhere n represents the
number of terms of the sequence being added.

Snis often called an nth
partial sum, since it can represent
the sum of a certain "part" of a sequence.

A series can be represented in
a compact form,
called summation notation, or
sigma notation.
The Greek capital letter sigma,
,
is used to indicate a sum.

"The summation from 1
to 4 of 3n":

Examples:

Problem:

Answer:

1. Evaluate:

2. Evaluate:

Notice how only the variable i
was replaced with the values from 2 to 4.

3. Evaluate:

Notice how raising (-1) to a power affected the signs of the
terms. This is an important pattern strategy to remember.

4. Evaluate:

While the starting value is usually 1, it can
actually be any integer value.

5. Use sigma notation to
represent
2 + 4 + 6 + 8 + ...
for 45 terms.

Look for a pattern
based upon the position of each term. In
this problem, each term is its position location
times 2, for a sequence formula of